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In dilute turbulent particle-laden flows, such as atmospheric dispersion ofpollutants or virus particles, the dynamics of tracer-like to low inertialparticles are significantly altered by the fluctuating motion of the carrierfluid phase. Neglecting the effects of fluid velocity fluctuations on particledynamics causes poor prediction of particle transport and dispersion. Toaccount for the effects of fluid phase fluctuating velocity on the particletransport, stochastic differential equations coupled with large-eddy simulationare proposed to model the fluid velocity seen by the particle. The drift anddiffusion terms in the stochastic differential equation are modelled usingneural networks ('neural stochastic differential equations'). The neuralnetworks are trained with direct numerical simulations (DNS) of decayinghomogeneous isotropic turbulence at low and moderate Reynolds numbers. Thepredictability of the proposed models are assessed against DNS results througha priori analyses and a posteriori simulations of decaying homogeneousisotropic turbulence at low-to-high Reynolds numbers. Total particlefluctuating kinetic energy is under-predicted by 40% with no model, compared tothe DNS data. In contrast, the proposed model predictions match total particlefluctuating kinetic energy to within 5% of the DNS data for low to high-inertiaparticles. For inertial particles, the model matches the variance ofuncorrelated particle velocity to within 10% of DNS results, compared to 60-70%under-prediction with no model. It is concluded that the proposed model isapplicable for flow configurations involving tracer and inertial particles,such as transport and dispersion of pollutants or virus particles.

Neural stochastic differential equations for particle dispersion in large-eddy simulations of homogeneous isotropic turbulence